Two Kinds of A Priori Infallibility Glen A. Hoffmann Ryerson University digital.library.ryerson.ca/object/144 Please Cite: Hoffmann, G. (2011). Two kinds of a priori infallibility. Synthese 181(2), 241-253. doi:10.1007/s11229-010-9800-9 library.ryerson.ca 1 Two Kinds of A Priori Infallibility On rationalist infallibilism, a wide range of both (i) analytic and (ii) synthetic a priori propositions can be infallibly justified (or absolutely warranted), i.e., justified to a degree that entails their truth and precludes their falsity. Though rationalist infallibilism is indisputably running its course, adherence to at least one of the two species of infallible a priori justification refuses to disappear from mainstream epistemology. Among others, Putnam (1978) still professes the a priori infallibility of some category (i) propositions, while Burge (1986, 1988, 1996) and Lewis (1996) have recently affirmed the a priori infallibility of some category (ii) propositions. In this paper, I take aim at rationalist infallibilism by calling into question the a priori infallibility of both analytic and synthetic propositions. The upshot will be twofold: first, rationalist infallibilism unsurprisingly emerges as a defective epistemological doctrine, and second, more importantly, the case for the a priori infallibility of one or both categories of propositions turns out to lack cogency. 1. Introduction: Rationalist Infallibilism On rationalist infallibilism, a wide range of both (i) analytic and (ii) synthetic a priori propositions can be infallibly or absolutely justified, i.e., justified to a degree that entails their truth and precludes their falsity. In particular, on this doctrine, at least two main classes of a priori propositions are susceptible of infallible justification: (i) logical, conceptual and mathematical propositions, and (ii) so-called self justifying propositions. Though rationalist infallibilism is undoubtedly running its course, adherence to at least one of the two species of infallible a priori justification refuses to disappear from mainstream epistemology. Among others, Putnam (1978) still professes the a priori infallibility of some category (i) propositions, 1 while Burge (1986, 1988, 1996), Lewis (1996) and Bealer (1999) have recently affirmed the a priori infallibility of some category (ii) propositions. 1 Of course, Putnam merely argues that there is at least one infallible a priori truth, what he calls ‘the minimal principle of contradiction’, leaving open whether there are others (1978, p. 155). Moreover, he claims that this a priori truth is infallibly justifiable in the sense that it is rationally impossible to disbelieve it (1978, pp. 155ff), a kind of infallibility that may or may not be covered by our definition. 2 In this paper, I take aim at rationalist infallibilism by disputing the a priori infallibility of both analytic and synthetic propositions. There will be two main outcomes of our inquiry. First, rationalist infallibilism predictably emerges as a fundamentally defective epistemological doctrine. Second, more importantly, the case for the a priori infallibility of one or both categories of propositions (erected by rationalists or empiricists) turns out to lack cogency. 2. Analytic Propositions The rationalist quest for infallible certitude often begins and sometimes ends with analytic propositions. There is a long tradition in philosophy, mathematics, the sciences and other disciplines of proclaiming the a priori infallibility of putative logical, conceptual and/or mathematical truths.2 While these are not mutually exclusive categories, the following kinds of examples have been tendered: (Logical Truth) Millie is either in the study or not in the study (M ~M), (Conceptual Truth) Jerry cannot both be a bachelor and married, (Conceptual Truth) Zoran cannot be in Moscow and London simultaneously, (Conceptual Truth) An object cannot be both blue and green all over at the same time, (Mathematical Truth) 2+3=5. In philosophy the infallibility thesis concerning analytic propositions is primarily associated with rationalists such as Descartes (1996) and Frege (1967, 1974), but has also been endorsed by empiricists such as Hume (1948), Putnam (1978), Ayer (1936, 1940, 1956), Carnap 2 See Boghossian (1994, p. 117ff) for a brief discussion of this history. 3 (1935, 1950) and some (other) proponents of logical positivism. Whether rationalist or empiricist, the case for the infallibility of logical, conceptual and mathematical propositions is essentially modal in character. At least some propositions in these domains, it is urged, are logically necessary (and thus infallibly justified) truths: they are true on all truth value assignments and false on no truth value assignment. Any straightforward employment of deductive reasoning, the claim runs, yields the transparency of this fact. On one standard formulation of the modal argument for analytic infallibility it is urged that some logical, conceptual and mathematical propositions have rigid meanings, meanings completely specifiable on the basis of syntactic and semantic principles.3 A superficial inspection of the syntax and semantics of sentences expressing such propositions, the reasoning runs, reveals they are true by meaning , and consequently, are necessary truths. For example, the mode of composition and the meaning of the lexical components of ‘Jerry cannot both be a bachelor and married’ are sufficient to yield the necessary truth, and corresponding infallibility, of the proposition expressed by this sentence. On another (related) variant of the modal argument it is urged that some logical, conceptual, and mathematical propositions have a special property concomitant with their rigid meaning: they make formally specifiable assertions, assertions whose meanings are wholly specifiable by syntactic and semantic principles (Cf. above).4 Since these propositions make formally specifiable assertions, the reasoning runs, they are susceptible of irrefutable proof by way of deductive logic (i.e., the universal laws of classical truth functional logic), a proof that cannot be overturned ex post facto . For example, a four row truth table or the application of two 3 This formulation of the argument is typically advanced in support of the analytic infallibility of so-called conceptual truths. It has been made in some form or another by Kant (1990), Ayer (1936, 1940), and Carnap (1935), among others. 4 This formulation of the argument is typically advanced in support of the analytic infallibility of so-called logical and mathematical truths. 4 rules of natural deduction supply irrevocable proof of any assertion of the form X ~X, by establishing its truth on any possible truth value assignment. In spite of its appeal at various periods in history, there is a seemingly decisive rebuttal to the modal argument for the infallibility of analytic propositions. Doubtless, it is acknowledged, some logical, conceptual and mathematical propositions are necessary truths and correspondingly conclusively justified within a specific logical/semantic framework. Presupposing classical truth functional logic, Millie is either in the study or not in the study is a necessary conclusively justified proposition. Presupposing a minimally acceptable semantic framework for logical and non-logical terms, 5 2+3=5, one cannot be a married bachelor, and an object cannot be blue and red all over at the same time are necessary conclusively justified propositions. The problem, evidently, is that propositions of this kind are not infallibly justifiable (or susceptible of absolute warrant), justifiable to a degree that is truth entailing and falsity precluding. Insofar as logical/semantic frameworks require some kind of confirmation in their own right, reason cannot infallibly justify elementary logical, conceptual and mathematical propositions (or apparently any other analytic proposition). In particular, deductive reasoning falls short in this case since inevitably it fails to establish the truth of the analytic propositions in question on any possible logic, semantics or interpretative standpoint.6 Deductive reasoning by its very nature cannot deliver analytic infallibility.7 5 By ‘minimally acceptable’ I have in mind a semantic framework in which, like all standard proposals, logical and non-logical terms have a determinate and consistent reference across all possible worlds. This would rule out bizarre Goodmanian-style logics in which ‘+’ might refer to the additive function except in cases where it follows ‘2’ where it will refer to the subtraction function or in which ‘bachelor’ refers to an adult unmarried male except in cases where that male is a cultural relativist. 6 This line of argument has a close kinship with the Quinean repudiation of analyticity (1953) since it impugns analytic infallibility on the basis of the logical defeasibility of all analytic propositions. Needless to say, though, it does not directly confront the viability of the analytic/synthetic distinction. 7 Although strictly speaking it has not been ruled out that there might be some other way to deliver analytic infallibility. 5 This well rehearsed line of argument enshrines a view of reason that on the surface looks compelling. In the long standing debate concerning epistemological infallibilism, stretching approximately from Plato to the present, an appealing principle has gained widespread recognition: reason cannot furnish absolute warrant for any analytic proposition. If reason is not an autonomous vehicle